The present invention relates to a ground analyzing system utilizing the characteristics of surface waves, particularly, Rayleigh waves.
In ground analysis performed in constructing the foundations of buildings, tunnels, and the faces of slope, geophysical analyzing methods have been used in many cases. Among the geophysical analyzing methods, particularly, an elastic wave analyzing method has been known as a method for quantitatively grasping the geotechnical properties of the ground. As representative elastic wave analyzing methods, a method using refracted waves and a method using direct waves have been known. According to the method using the refracted waves, the geotechnical properties of the ground are extensively grasped. According to the method using the direct waves, the geotechnical properties of the ground are locally grasped. The method using direct waves utilizes a boring hole. Both the methods use P waves and S waves called body waves among elastic undulation generated from a vibration source. The P waves are also called compression waves while the S waves are also called shear waves. Those waves are properly used in consideration of geological conditions.
Other than the P waves and the S waves, waves called surface waves have been known. It has also been known that the surface wave accompanies with a dispersing phenomenon and has such properties that the propagation velocity thereof depends on the wavelength thereof.
The properties of the surface wave will now be described hereinbelow in brief. When a vibration source applies a vibration to the surface of the ground in the vertical direction, waves called the surface waves occur in the ground in addition to the P waves and the S waves. The P waves and the S waves propagate hemispherically from the vibration source. On the other hand, Rayleigh waves among the surface waves propagate so as to extend the diameter of a cylinder having a predetermined height defined by a frequency. In other words, each of the P wave and the S wave generated from the vibration source has the directivity. The P wave traveling below the vibration source has the maximum energy. The S wave traveling in the direction of 45xc2x0 has the maximum energy. In other words, the P wave and the S wave hardly transmit in the horizontal direction. Consequently, only the surface wave can apply the large amplitude of the vibration to the surface of the ground.
The geometrical attenuation coefficient of each of the P wave and the S wave denotes rxe2x88x921 (r indicates a distance) in the lower direction but the geometrical attenuation coefficient thereof denotes rxe2x88x922 in the vicinity of the ground surface.
On the other hand, the geometrical attenuation coefficient of the surface wave denotes rxe2x88x920.5 on the surface of the ground. In addition to the Rayleigh waves, the surface waves include Love waves, P-P mode waves similar to the P waves, and plate waves. In the present invention, the Rayleigh waves are used.
FIG. 1 shows the relationship between the velocities of the Rayleigh wave, the P wave, and the S wave. Three types of velocity ratios vary depending on the Poisson""s ratio of soil comprising the ground. The velocity of the S wave denotes a value that is approximate to that of the Rayleigh wave. Referring to FIG. 1, the axis of ordinates denotes a value expressed by an equation of V/Vs=Vxc2x7(xcfx81/G)1/2. Reference symbol Vs denotes the velocity of the S wave, reference symbol xcfx81 denotes the density of soil, reference symbol G indicates the modulus of rigidity, and reference symbol V indicates the velocity of the P wave or the Rayleigh wave.
Since the velocity of the Rayleigh wave is approximate to that of the S wave and typically denotes a geotechnical value, the respective geotechnical values of the S wave and the Rayleigh wave can be estimated using a correlation equation between the velocity of the S wave and an N value (standard penetration test value) or a correlation equation between the velocity of the S wave and a qa value (allowable bearing capacity).
On the basis of the above-mentioned findings, it is an object of the present invention to provide a ground analyzing system, which can perform a nondestructive, accurate, rapid, and economical analysis using the dispersing properties of surface waves, particularly, Rayleigh waves.
A ground analyzing system according to the present invention is for carrying out ground analysis by detecting surface waves generated by vibrating the surface of the ground in the vertical direction. According to an aspect of the present invention, the ground analyzing system includes: first and second acceleration detectors disposed at a distance L from each other on the ground; a measuring instrument including a seismometer unit for receiving detection signals from the first and second acceleration detectors to generate first and second acceleration time-series signals; and a signal processing unit for receiving the first and second acceleration time-series signals to perform a signal processing based on a predetermined analysis program. The signal processing unit performs Fourier transform to calculate power spectra and a cross spectrum and also calculates a transfer function H(f) using the calculated power spectrum and cross spectrum. The signal processing unit also calculates a phase difference xcex94xcex8(f) between the first and second acceleration time-series signals and a time difference xcex94t(f) therebetween using the calculated transfer function. The signal processing unit further calculates a mean propagation velocity Vr(f) of the surface waves and a depth D(f) on the basis of the calculated time difference xcex94t(f) and the distance L.
According to the present invention, there is provided a recording medium which has recorded an analysis program for processing first and second acceleration time-series signals obtained by detecting surface waves, generated by vibrating the surface of the ground in the vertical direction, at two points arranged at a distance from each other. According to the present invention, the recording medium has recorded the analysis program for executing the steps of: performing Fourier transform to the first and second acceleration time-series signals to calculate power spectra and a cross spectrum; calculating a transfer function H(f) using the calculated power spectrum and cross spectrum; calculating a phase difference xcex94xcex8(f) between the first and second acceleration time-series signals and a time difference xcex94t(f) therebetween on the basis of the calculated transfer function H(f); and calculating a mean propagation velocity Vr(f) of the surface waves and a depth D(f) on the basis of the calculated time difference xcex94t(f) and the distance L.